Prepare the filling: Heat the vegetable oil in a small, non-stick frying pan over a medium heat. Add the diced onion and cook for 2 minutes, until it turns translucent and releases a sweet, mellow aroma. Add the diced green and red peppers and cook for another 2–3 minutes, until they soften and smell fragrant. Toss in the diced chicken or turkey and cook for 1 minute, just to warm it through. The pan should look vibrant and the edges of the vegetables will be just beginning to brown. Transfer this mixture to a bowl and set aside. Wipe the pan clean with a piece of kitchen roll.

Whisk the eggs: Crack the eggs into a medium bowl. Add the milk or cream, salt, and a good grind of black pepper. Whisk vigorously with a fork or a small whisk for about 30 seconds. You are looking for a uniform, pale yellow liquid with no visible streaks of white. The mixture should feel light and airy, and you'll hear the bubbles popping as you whisk.

Heat the pan: Place the clean, non-stick pan back over a medium-low heat. Add the butter and let it melt slowly, tilting the pan to coat the entire base. The butter should foam gently but not brown—if it sizzles loudly or turns brown, your heat is too high. The kitchen will fill with a nutty, creamy scent.

Pour in the eggs: Once the butter has melted and the foam has subsided slightly, pour the whisked eggs into the centre of the pan. Let them settle for a few seconds, then use a silicone spatula to gently stir the eggs in a circular motion, dragging the cooked edges towards the centre. Do this for about 20 seconds, until the eggs are about 70% set but still look soft and glossy on top. The sound will shift from a loud sizzle to a gentle, quiet hiss.

Add the filling: Smooth the surface of the eggs with your spatula. Spoon the cooked filling evenly over one half of the omelette. Sprinkle the grated cheese over the filling, if using. The eggs should still look slightly wet and custardy around the edges—this is the sign of a tender omelette.

Fold and finish: Use your spatula to carefully lift the empty half of the omelette and fold it over the filling. Gently press down on the top to seal. Let it cook for another 30–45 seconds. The base should be a light golden brown and the omelette should feel firm but give slightly when you press it. The aroma will be a wonderful blend of buttery eggs, sweet peppers, and savoury meat.

Slide and serve: Tilt the pan over a warm plate and gently slide the omelette out, seam-side down. The surface should be glossy and smooth, with a delicate, golden-brown underside. Serve immediately, while the cheese is still molten and the eggs are perfectly tender.